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21st Century Lessons
Combining Like Terms
1
Warm Up
OBJECTIVE: Students will be able to determine if expressions are equivalent by
combining like terms.
Language Objective: Students will be able to explain in words how to combine
like terms.
True or False? Explain your answer.
a. 5 + 5 = 2 · 5
True
b. 3· 7 = 7 + 7 + 7
c. 6 + 6 + 6 + 6 = 6 · 6
True
False
d. x + x + x = 3x
True
Agenda
2
Agenda:
OBJECTIVE: Students will be able to determine if expressions are equivalent by
combining like terms.
Language Objective: Students will be able to explain in words how to combine
like terms.
1) Warm Up
2) Launch
True or False?- Individual
What is the Area?- Whole Class
5 minutes
3) Explore
Using Tiles- Partners
17 minutes
18 minutes
4) Summary
No Tiles, Vocabulary, Process,
Quick Check- Partners, Whole Class
5) Practice
Partners
6) Assessment Exit Slip- Individual
3
5 minutes
15 minutes
5 minutes
Launch- What is the Area?
What is the area of the
rectangle?
x
A = l× w
x
4x
4
3x
4
7x
x
47 +
3
Area = 4x + 3x
3
3
Area = 7x
4x + 3x = 7x
Agenda
4
Explore- Using Tiles
Think back to the warm up x + x + x = 3x.
Let each x represent a red tile.
We just
So, how many tiles would we need?
x
x
x
= 3x
combined all
the x’s!
Can we represent 3x another way using
tiles?
x
x + x
Definition
5
= 2x + x = 3x
Agenda
Explore- Using Tiles
Using your tiles, what would you get
if you combined 2x + 4x?
x
x
x
x
+
x
x
x
x
x
x
x
x
Now
combine!
= 6x
Is this the only way to show 6x?
Agenda
7
Explore- Using Tiles
Is this the only way to show 6x?
x
x
x
+
x
x
x
5x
More
Practice
8
x
x
x
3x = 6x
+ x
+
1x = 6x
+
3x
x
x
Agenda
Explore- Using Tiles
What would you get if you combined
5x + 3y + 2x + y? Use your tiles.
x x x x x+ y y y+ x x +y y
7x + 4y
5x + 3y + 2x + y = 7x + 4y
Agenda
10
Summary- No Tiles
How can we combine 5x + 3y + 2x + y
without using tiles?
5x + 3y + 2x + y
Identify variables
that are the same
Commutative
Property
Now Combine!
7x + 4 y
5x + 3y + 2x + y = 7x + 4y
Agenda
11
Summary- Vocabulary
Example
5x + 3y + 2x + y
• Term: a single number, variable, or number
and variables multiplied together.
5x 3y 2x y
are terms in this expression.
• Like Terms: terms that have the same
variable or power.
5x and 2x
3y and y
Agenda
12
Summary- Process
1. Copy the expression
2. Identify the like terms
5x + 3y + 2x + y
5x ++3y
5x
3y++2x2x+ y+ y
3. Rewrite using the
Commutative Property
4. Combine the variables
that are the same
7x + 4y
Agenda
13
Summary- Quick Check
With your partner, write an equivalent
expression for the following:
#1. 4a + 6b + 3a + 9b 7a + 15b
#2. 15x – 4x + 12
11x + 12
#3. y + y + y
#4. 5y + 7z
3y
Click for
definition
14
5y + 7z
Agenda
Practice- Partners
I. Model the following expression by
drawing squares.
Let
=x
=y
a. 6x + 2y
+
b. 4x + y + 5y + 2x
+
+
+
Agenda
16
Practice- Partners
II. Explain why the following statement is
true.
2x + 4y ¹ 6xy
2x and 4y are not like terms, therefore, you
cannot combine them.
Another
Explanation
17
Agenda
Practice- Partners
III. Write an equivalent expression for the
following expressions.
1. 5a + 6a +10
11a +10
2. x + 9y +12x
13x + 9y
3. 13a - 8a + 9b - 4b
5a - 5b
Agenda
19
Practice- Partners
IV. Explain Yvonne’s mistake in the following
problem.
8x + 6x + 2 =16x
Yvonne just added all the numbers
together. She can add numbers that are
the like terms, 8x and 6x, but not 2 since it
does not have an x.
Agenda
20
Assessment- Exit Slip
Jose and Amy were asked to combine 7x + 2y + 6y + 3x.
Decide who is correct. Explain.
Jose
7x + 2y + 6y + 3x
Jose’s work
7x + 3x + 2y + 6y
10x + 8y
18xy
7x + 2y + 6y + 3x = 18xy
Amy
7x + 2y + 6y + 3x
Amy’s work
7x + 3x + 2y + 6y
10x + 8y
7x + 2y + 6y + 3x = 10x + 8y
Agenda
21